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Abstract

The exploration problem is a central issue in mobile robotics. A complete terrain coverage is not practical if the environment is large with only a few small hotspots. This paper presents an adaptive multi-robot exploration strategy that is novel in performing both wide-area coverage and hotspot sampling using non-myopic path planning. As a result, the environmental phenomena can be accurately mapped. It is based on a dynamic programming formulation, which we call the Multi-robot Adaptive Sampling Problem (MASP). A key feature of MASP is in covering the entire adaptivity spectrum, thus allowing strategies of varying adaptivity to be formed and theoretically analyzed in their performance; a more adaptive strategy improves mapping accuracy. We apply MASP to sampling the Gaussian and log-Gaussian processes, and analyze if the resulting strategies are adaptive and maximize wide-area coverage and hotspot sampling. Solving MASP is non-trivial as it comprises continuous state components. So, it is reformulated for convex analysis, which allows discrete-state monotone-bounding approximation to be developed. We provide a theoretical guarantee on the policy quality of the approximate MASP (aMASP) for using in MASP. Although aMASP can be solved exactly, its state size grows exponentially with the number of stages. To alleviate this computational difficulty, anytime algorithms are proposed based on aMASP, one of which can guarantee its policy quality for MASP in real time.